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Answer :
Sure, let's use the Distributive Property to multiply the polynomials step-by-step.
We are given:
[tex]\[ 3x^2(2x^4 - 15x) \][/tex]
Using the Distributive Property, we will multiply each term inside the parentheses by [tex]\(3x^2\)[/tex].
Step 1:
Multiply [tex]\(3x^2\)[/tex] by the first term inside the parentheses, which is [tex]\(2x^4\)[/tex].
[tex]\[ 3x^2 \cdot 2x^4 = 6x^6 \][/tex]
Step 2:
Multiply [tex]\(3x^2\)[/tex] by the second term inside the parentheses, which is [tex]\(-15x\)[/tex].
[tex]\[ 3x^2 \cdot -15x = -45x^3 \][/tex]
Step 3:
Add the results from Step 1 and Step 2 together.
[tex]\[
6x^6 - 45x^3
\][/tex]
Therefore, the expression [tex]\(3x^2(2x^4 - 15x)\)[/tex] simplifies to:
[tex]\[
6x^6 - 45x^3
\][/tex]
So, the final answer is:
[tex]\[ 6x^6 - 45x^3 \][/tex]
We are given:
[tex]\[ 3x^2(2x^4 - 15x) \][/tex]
Using the Distributive Property, we will multiply each term inside the parentheses by [tex]\(3x^2\)[/tex].
Step 1:
Multiply [tex]\(3x^2\)[/tex] by the first term inside the parentheses, which is [tex]\(2x^4\)[/tex].
[tex]\[ 3x^2 \cdot 2x^4 = 6x^6 \][/tex]
Step 2:
Multiply [tex]\(3x^2\)[/tex] by the second term inside the parentheses, which is [tex]\(-15x\)[/tex].
[tex]\[ 3x^2 \cdot -15x = -45x^3 \][/tex]
Step 3:
Add the results from Step 1 and Step 2 together.
[tex]\[
6x^6 - 45x^3
\][/tex]
Therefore, the expression [tex]\(3x^2(2x^4 - 15x)\)[/tex] simplifies to:
[tex]\[
6x^6 - 45x^3
\][/tex]
So, the final answer is:
[tex]\[ 6x^6 - 45x^3 \][/tex]
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